Is there a way to visualize the tris of a scene?
Selecting All Triangles

You can use the MeshLint add-on to select all the triangular faces in your mesh. 

Another way is to select a triangular face, Select Similar ShiftG > Polygon Sides and this will select all tris.



Rotating Edges

If you have a mesh where the quads have been converted to tris you can "turn" or "rotate" the orientation of the edge within that triangulated quad.

For example, in the screen shot below there is a Suzanne mesh that has been converted to all tris using the Triangulate Modifier. In Edit Mode if we select an edge that bisects a quad we can then press CtrlE and from the contextual menu choose Rotate Edge CW or Rotate Edge CCW depending on whether you want Clockwise or Counter-Clockwise rotation (for a triangulated quad it makes no difference which you choose, the result is the same).



Further details

This operation can also be accessed from the menu under Mesh > Edges. It can be performed in all three selection modes (Vertex / Edge / Face).

If you plan to do this operation many times repeatedly it would probably be best to assign a keyboard shortcut to it. While the contextual menu is open you can right click on the menu items and assign shortcuts.

An example utilizing the Mac's "Command" modifier key: